Models of passive and active dendrite motoneuron pools and their differences in muscle force control

Onion skin is not a universal firing pattern for spinal motoneurons: simulation study

Muscle force is modulated by sequential recruitment and firing rates of motor units (MUs). However, discrepancies exist in the literature regarding the relationship between MU firing rates and their recruitment, presenting two contrasting firing-recruitment schemes. The first firing scheme, known as "onion skin," exhibits low-threshold MUs firing faster than high-threshold MUs, forming separate layers akin to an onion. This contradicts the other firing scheme, known as "reverse onion skin" or "afterhyperpolarization (AHP)," with low-threshold MUs firing slower than high-threshold MUs. To study this apparent dichotomy, we used a high-fidelity computational model that prioritizes physiological fidelity and heterogeneity, allowing versatility in the recruitment of different motoneuron types. Our simulations indicate that these two schemes are not mutually exclusive but rather coexist. The likelihood of observing each scheme depends on factors such as the motoneuron pool activation level, synaptic input activation rates, and MU type. The onion skin scheme does not universally govern the encoding rates of MUs but tends to emerge in unsaturated motoneurons (cells firing < their fusion frequency that generates peak force), whereas the AHP scheme prevails in saturated MUs (cells firing at their fusion frequency), which is highly probable for slow (S)-type MUs. When unsaturated, fast fatigable (FF)-type MUs always show the onion skin scheme, whereas S-type MUs do not show either one. Fast fatigue-resistant (FR)-type MUs are generally similar but show weaker onion skin behaviors than FF-type MUs. Our results offer an explanation for the longstanding dichotomy regarding MU firing patterns, shedding light on the factors influencing the firing-recruitment schemes.NEW & NOTEWORTHY The literature reports two contrasting schemes, namely the onion skin and the afterhyperpolarization (AHP) regarding the relationship between motor units (MUs) firing rates and recruitment order. Previous studies have examined these schemes phenomenologically, imposing one scheme on the firing-recruitment relationship. Here, we used a high-fidelity computational model that prioritizes biological fidelity and heterogeneity to investigate motoneuron firing schemes without bias toward either scheme. Our objective findings offer an explanation for the longstanding dichotomy on MU firing patterns.

Skeletal muscle models composed of motor units: A review

The mathematical muscle models should include several aspects of muscle structure and physiology. First, muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties and play different roles in generating muscle force. Second, whole muscle activity is an effect of net excitatory inputs to a pool of motoneurons innervating the muscle, which have different excitability, influencing MU recruitment. In this review, we compare various methods for modeling MU twitch and tetanic forces and then discuss muscle models composed of different MU types and number. We first present four different analytical functions used for twitch modeling and show limitations related to the number of twitch describing parameters. We also show that a nonlinear summation of twitches should be considered in modeling tetanic contractions. We then compare different muscle models, most of which are variations of Fuglevand's model, adopting a common drive hypothesis and the size principle. We pay attention to integrating previously developed models into a consensus model based on physiological data from in vivo experiments on the rat medial gastrocnemius muscle and its respective motoneurons. Finally, we discuss the shortcomings of existing models and potential applications for studying MU synchronization, potentiation, and fatigue.

Effects of voluntary contraction on the soleus H-reflex of different amplitudes in healthy young adults and in the elderly

A number of H-reflex studies used a moderate steady voluntary contraction in an attempt to keep the motoneuron pool excitability relatively constant. However, it is not clear whether the voluntary muscle activation itself represents a confounding factor for the elderly, as a few ongoing mechanisms of reflex modulation might be compromised. Further, it is well-known that the amount of either inhibition or facilitation from a given conditioning depends on the size of the test H-reflex. The present study aimed at evaluating the effects of voluntary contraction over a wide range of reflex amplitudes. A significant reflex facilitation during an isometric voluntary contraction of the soleus muscle (15% of the maximal voluntary isometric contraction-MVC) was found for both young adults and the elderly (p < 0.05), regardless of their test reflex amplitudes (considering the ascending limb of the H-reflex recruitment curve-RC). No significant difference was detected in the level of reflex facilitation between groups for all the amplitude parameters extracted from the RC. Simulations with a computational model of the motoneuron pool driven by stationary descending commands yielded qualitatively similar amount of reflex facilitation, as compared to human experiments. Both the experimental and modeling results suggest that possible age-related differences in spinal cord mechanisms do not significantly influence the reflex modulation during a moderate voluntary muscle activation. Therefore, a background voluntary contraction of the ankle extensors (e.g., similar to the one necessary to maintain upright stance) can be used in experiments designed to compare the RCs of both populations. Finally, in an attempt to elucidate the controversy around changes in the direct motor response (M-wave) during contraction, the maximum M-wave (Mmax) was compared between groups and conditions. It was found that the Mmax significantly increases (p < 0.05) during contraction and decreases (p < 0.05) with age arguably due to muscle fiber shortening and motoneuron loss, respectively.

Electrophysiological and functional signs of Guillain-Barré syndrome predicted by a multiscale neuromuscular computational model

Objective. The diagnosis of nerve disorders in humans has relied heavily on the measurement of electrical signals from nerves or muscles in response to electrical stimuli applied at appropriate locations on the body surface. The present study investigated the demyelinating subtype of Guillain-Barré syndrome using multiscale computational model simulations to verify how demyelination of peripheral axons may affect plantar flexion torque as well as the ongoing electromyogram (EMG) during voluntary isometric or isotonic contractions. Approach. Changes in axonal conduction velocities, mimicking those found in patients with the disease at different stages, were imposed on a multiscale computational neuromusculoskeletal model to simulate subjects performing unipodal plantar flexion force and position tasks. Main results. The simulated results indicated changes in the torque signal during the early phase of the disease while performing isotonic tasks, as well as in torque variability after partial conduction block while performing both isometric and isotonic tasks. Our results also indicated changes in the root mean square values and in the power spectrum of the soleus EMG signal as well as changes in the synchronisation index computed from the firing times of the active motor units. All these quantitative changes in functional indicators suggest that the adoption of such additional measurements, such as torques and ongoing EMG, could be used with advantage in the diagnosis and be relevant in providing extra information for the neurologist about the level of the disease. Significance. Our findings enrich the knowledge of the possible ways demyelination affects force generation and position control during plantarflexion. Moreover, this work extends computational neuroscience to computational neurology and shows the potential of biologically compatible neuromuscular computational models in providing relevant quantitative signs that may be useful for diagnosis in the clinic, complementing the tools traditionally used in neurological electrodiagnosis.

Optimization framework for the model-based estimation of in vivo α-motoneuron properties in the intact human

The in vivo estimation of α-motoneuron (MN) properties in humans is crucial to characterize the effect that neurorehabilitation technologies may elicit over the composite neuro-musculoskeletal system. Here, we combine biophysical neuronal modelling, high-density electromyography and convolutive blind-source separation along with numerical optimization to estimate geometrical and electrophysiological properties of in vivo decoded human MNs. The proposed methodology implements multi-objective optimization to automatically tune ionic channels conductance and soma size of MN models for minimizing the error between several features of simulated and in vivo decoded MN spike trains. This approach will open new avenues for the closed-loop control of motor restorative technologies such as wearable robots and neuromodulation devices.Clinical Relevance- This work proposes a non-invasive framework for the in vivo estimation of person-specific α-motoneuron properties. This will enable predicting neuronal adaptations in response to neurorehabilitation therapies in the intact human.

Sex Steroids as Regulators of Gestural Communication

Gestural communication is ubiquitous throughout the animal kingdom, occurring in species that range from humans to arthropods. Individuals produce gestural signals when their nervous system triggers the production of limb and body movement, which in turn functions to help mediate communication between or among individuals. Like many stereotyped motor patterns, the probability of a gestural display in a given social context can be modulated by sex steroid hormones. Here, we review how steroid hormones mediate the neural mechanisms that underly gestural communication in humans and nonhumans alike. This is a growing area of research, and thus we explore how sex steroids mediate brain areas involved in language production, social behavior, and motor performance. We also examine the way that sex steroids can regulate behavioral output by acting in the periphery via skeletal muscle. Altogether, we outline a new avenue of behavioral endocrinology research that aims to uncover the hormonal basis for one of the most common modes of communication among animals on Earth.

Neurophysiological correlates of force control improvement induced by sinusoidal vibrotactile stimulation

OBJECTIVE

An optimal level of vibrotactile stimulation has been shown to improve sensorimotor control in healthy and diseased individuals. However, the underlying neurophysiological mechanisms behind the enhanced motor performance caused by vibrotactile stimulation are yet to be fully understood. Therefore, here we aim to evaluate the effect of a cutaneous vibration on the firing behavior of motor units in a condition of improved force steadiness.

APPROACH

Participants performed a visuomotor task, which consisted of low-intensity isometric contractions of the first dorsal interosseous (FDI) muscle, while sinusoidal (175 Hz) vibrotactile stimuli with different intensities were applied to the index finger. High-density surface electromyogram was recorded from the FDI muscle, and a decomposition algorithm was used to extract the motor unit spike trains. Additionally, computer simulations were performed using a multiscale neuromuscular model to provide a potential explanation for the experimental findings.

MAIN RESULTS

Experimental outcomes showed that an optimal level of vibration significantly improved force steadiness (estimated as the coefficient of variation of force). The decreased force variability was accompanied by a reduction in the variability of the smoothed cumulative spike train (as an estimation of the neural drive to the muscle), and the proportion of common inputs to the FDI motor nucleus. However, the interspike interval variability did not change significantly with the vibration. A mathematical approach, together with computer simulation results suggested that vibrotactile stimulation would reduce the variance of the common synaptic input to the motor neuron pool, thereby decreasing the low frequency fluctuations of the neural drive to the muscle and force steadiness.

SIGNIFICANCE

Our results demonstrate that the decreased variability in common input accounts for the enhancement in force control induced by vibrotactile stimulation.

A computer simulation study on the influences of loss and damage of primary muscle spindle afferents on soleus muscle stretch reflex

Sensory loss is detrimental to sensorimotor control. Several studies have reported that loss and/or damage of primary (Ia) muscle spindle afferents significantly influence the stretch reflex responses of leg and foot muscles. However, a systematic experimental evaluation on how the impairment of Ia muscle spindle afferents affects the stretch reflex is difficult due to technical and ethical issues. In the present study, the aim was to use computer simulations of a multiscale neuromusculoskeletal model to investigate how changes in: i) the number of Ia afferents, ii) the synaptic conductance between Ia sensory fibers and spinal motor neurons (MNs), and iii) the conduction velocities (CVs) of Ia afferents, would influence the stretch reflex of a leg muscle (soleus). Simulation results showed that both anatomical and functional loss of Ia afferents exerted an influence on the amplitude of short-latency stretch reflex response (M1) and the late phase of medium-latency response (M2). Additionally, changes in CVs of Ia afferents mainly influenced the latency of M1 and the amplitude of M2. Our findings provide conceptual evidence that a combination of anatomical and functional loss, as well as changes in CVs of Ia afferents due to demyelination, can explain the stretch reflex responses observed in peripheral neuropathies.

Curated Model Development Using NEUROiD: A Web-Based NEUROmotor Integration and Design Platform

Decades of research on neuromotor circuits and systems has provided valuable information on neuronal control of movement. Computational models of several elements of the neuromotor system have been developed at various scales, from sub-cellular to system. While several small models abound, their structured integration is the key to building larger and more biologically realistic models which can predict the behavior of the system in different scenarios. This effort calls for integration of elements across neuroscience and musculoskeletal biomechanics. There is also a need for development of methods and tools for structured integration that yield larger in silico models demonstrating a set of desired system responses. We take a small step in this direction with the NEUROmotor integration and Design (NEUROiD) platform. NEUROiD helps integrate results from motor systems anatomy, physiology, and biomechanics into an integrated neuromotor system model. Simulation and visualization of the model across multiple scales is supported. Standard electrophysiological operations such as slicing, current injection, recording of membrane potential, and local field potential are part of NEUROiD. The platform allows traceability of model parameters to primary literature. We illustrate the power and utility of NEUROiD by building a simple ankle model and its controlling neural circuitry by curating a set of published components. NEUROiD allows researchers to utilize remote high-performance computers for simulation, while controlling the model using a web browser.

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

The effects of model composition design choices on high-fidelity simulations of motoneuron recruitment and firing behaviors

OBJECTIVE

Computational models often require tradeoffs, such as balancing detail with efficiency; yet optimal balance should incorporate sound design features that do not bias the results of the specific scientific question under investigation. The present study examines how model design choices impact simulation results.

APPROACH

We developed a rigorously-validated high-fidelity computational model of the spinal motoneuron pool to study three long-standing model design practices which have yet to be examined for their impact on motoneuron recruitment, firing rate, and force simulations. The practices examined were the use of: (1) generic cell models to simulate different motoneuron types, (2) discrete property ranges for different motoneuron types, and (3) biological homogeneity of cell properties within motoneuron types.

MAIN RESULTS

Our results show that each of these practices accentuates conditions of motoneuron recruitment based on the size principle, and minimizes conditions of mixed and reversed recruitment orders, which have been observed in animal and human recordings. Specifically, strict motoneuron orderly size recruitment occurs, but in a compressed range, after which mixed and reverse motoneuron recruitment occurs due to the overlap in electrical properties of different motoneuron types. Additionally, these practices underestimate the motoneuron firing rates and force data simulated by existing models.

SIGNIFICANCE

Our results indicate that current modeling practices increase conditions of motoneuron recruitment based on the size principle, and decrease conditions of mixed and reversed recruitment order, which, in turn, impacts the predictions made by existing models on motoneuron recruitment, firing rate, and force. Additionally, mixed and reverse motoneuron recruitment generated higher muscle force than orderly size motoneuron recruitment in these simulations and represents one potential scheme to increase muscle efficiency. The examined model design practices, as well as the present results, are applicable to neuronal modeling throughout the nervous system.

PyMUS: Python-Based Simulation Software for Virtual Experiments on Motor Unit System

We constructed a physiologically plausible computationally efficient model of a motor unit and developed simulation software that allows for integrative investigations of the input-output processing in the motor unit system. The model motor unit was first built by coupling the motoneuron model and muscle unit model to a simplified axon model. To build the motoneuron model, we used a recently reported two-compartment modeling approach that accurately captures the key cell-type-related electrical properties under both passive conditions (somatic input resistance, membrane time constant, and signal attenuation properties between the soma and the dendrites) and active conditions (rheobase current and afterhyperpolarization duration at the soma and plateau behavior at the dendrites). To construct the muscle unit, we used a recently developed muscle modeling approach that reflects the experimentally identified dependencies of muscle activation dynamics on isometric, isokinetic and dynamic variation in muscle length over a full range of stimulation frequencies. Then, we designed the simulation software based on the object-oriented programing paradigm and developed the software using open-source Python language to be fully operational using graphical user interfaces. Using the developed software, separate simulations could be performed for a single motoneuron, muscle unit and motor unit under a wide range of experimental input protocols, and a hierarchical analysis could be performed from a single channel to the entire system behavior. Our model motor unit and simulation software may represent efficient tools not only for researchers studying the neural control of force production from a cellular perspective but also for instructors and students in motor physiology classroom settings.

Impact of the localization of dendritic calcium persistent inward current on the input-output properties of spinal motoneuron pool: a computational study

The goal of this study is to investigate how the dendritic Ca-PIC location influences nonlinear input-output properties and depends on the type of motoneurons across the motoneuron pool. A model motoneuron pool consisting of 10 motoneurons was constructed using a recently developed two-compartment modeling approach that reflected key cell type-associated properties experimentally identified. The dendritic excitability and firing output depended systematically on both the PIC location and the motoneuron type. The PIC onset and offset in the current-voltage (I-V) relationship tended to occur at more hyperpolarized voltages as the path length to the PIC channels from the soma increased and as the cell type shifted from high- to low-threshold motoneurons. At the same time, the firing acceleration and frequency hysteresis in the frequency-current (F-I) relationship became faster and larger, respectively. However, the PIC onset-offset hysteresis increased as the path length and the recruitment threshold increased. Furthermore, the gain of frequency-current function before full PIC activation was larger for PIC channels located over distal dendritic regions in low- compared with high-threshold motoneurons. When compared with previously published experimental observations, the modeling concurred when Ca-PIC channels were placed closer to the soma in high- than low-threshold motoneurons in the model motoneuron pool. All of these results suggest that the negative relationship of Ca-PIC location and cell recruitment threshold may underlie the systematic variation in I-V and F-I transformation across the motoneuron pool.NEW & NOTEWORTHY How does the dendritic location of calcium persistent inward current (Ca-PIC) influence dendritic excitability and firing behavior across the spinal motoneuron pool? This issue was investigated developing a model motoneuron pool that reflected key motoneuron type-specific properties experimentally identified. The simulation results point out the negative relationship between the distance of Ca-PIC source from the soma and cell recruitment threshold as a basis underlying the systematic variation in input-output properties of motoneurons over the motoneuron pool.

Nonlinear Frequency-Domain Analysis of the Transformation of Cortical Inputs by a Motoneuron Pool-Muscle Complex

Corticomotor coherence in the beta and/or gamma bands has been described in different motor tasks, but the role of descending brain oscillations on force control has been elusive. Large-scale computational models of a motoneuron pool and the muscle it innervates have been used as tools to advance the knowledge of how neural elements may influence force control. Here, we present a frequency domain analysis of a NARX model fitted to a large-scale neuromuscular model by the means of generalized frequency response functions (GFRF). The results of such procedures indicated that the computational neuromuscular model was capable of transforming an oscillatory synaptic input (e.g., at 20 Hz) into a constant mean muscle force output. The nonlinearity uncovered by the GFRFs of the NARX model was responsible for the demodulation of an oscillatory input (e.g., a beta band oscillation coming from the brain and forming the input to the motoneuron pool). This suggests a manner by which brain rhythms descending as command signals to the spinal cord and acting on a motoneuron pool can regulate a maintained muscle force. In addition to the scientific aspects of these results, they provide new interpretations that may further neural engineering applications associated with quantitative neurological diagnoses and robotic systems for artificial limbs.

Muscle length-dependent contribution of motoneuron Cav1.3 channels to force production in model slow motor unit

Persistent inward current (PIC)-generating Ca_v1.3 channels in spinal motoneuron dendrites are thought to be actively recruited during normal behaviors. However, whether and how the activation of PIC channels influences force output of motor unit remains elusive. Here, building a physiologically realistic model of slow motor unit I demonstrated that force production induced by the PIC activation is much smaller for short than lengthened muscles during the regular firing of the motoneuron that transitions from the quiescent state by either a brief current pulse at the soma or a brief synaptic excitation at the dendrites. By contrast, the PIC-induced force potentiation was maximal for short muscles when the motoneuron switched from a stable low-frequency firing state to a stable high-frequency firing state by the current pulse at the soma. Under the synaptic excitation at the dendrites, however, the force could not be potentiated by the transitioning of the motoneuron from a low- to a high-frequency firing state due to the simultaneous onset of PIC at the dendrites and firing at the soma. The strong dependency of the input-output relationship of the motor unit on the neuromodulation and Ia afferent inputs for the PIC channels was further shown under static variations in muscle length. Taken together, these findings suggest that the PIC activation in the motoneuron dendrites may differentially affect the force production of the motor unit, depending not only on the firing state history of the motoneuron and the variation in muscle length but also on the mode of motor activity.NEW & NOTEWORTHY Ca_v1.3 channels in motoneuron dendrites are actively involved during normal motor activities. To investigate the effects of the activation of motoneuron Ca_v1.3 channels on force production, a model motor unit was built based on best-available data. The simulation results suggest that force potentiation induced by Ca_v1.3 channel activation is strongly modulated not only by firing history of the motoneuron but also by length variation of the muscle as well as neuromodulation inputs from the brainstem.

Reassessment of Non-Monosynaptic Excitation from the Motor Cortex to Motoneurons in Single Motor Units of the Human Biceps Brachii

Corticospinal excitation is mediated by polysynaptic pathways in several vertebrates, including dexterous monkeys. However, indirect non-monosynaptic excitation has not been clearly observed following transcranial electrical stimulation (TES) or cervicomedullary stimulation (CMS) in humans. The present study evaluated indirect motor pathways in normal human subjects by recording the activities of single motor units (MUs) in the biceps brachii (BB) muscle. The pyramidal tract was stimulated with weak TES, CMS, and transcranial magnetic stimulation (TMS) contralateral to the recording side. During tasks involving weak co-contraction of the BB and hand muscles, all stimulation methods activated MUs with short latencies. Peristimulus time histograms (PSTHs) showed that responses with similar durations were induced by TES (1.9 ± 1.4 ms) and CMS (2.0 ± 1.4 ms), and these responses often showed multiple peaks with the PSTH peak having a long duration (65.3% and 44.9%, respectively). Such long-duration excitatory responses with multiple peaks were rarely observed in the finger muscles following TES or in the BB following stimulation of the Ia fibers. The responses obtained with TES were compared in the same 14 BB MUs during the co-contraction and isolated BB contraction tasks. Eleven and three units, respectively, exhibited activation with multiple peaks during the two tasks. In order to determine the dispersion effects on the axon conduction velocities (CVs) and synaptic noise, a simulation study that was comparable to the TES experiments was performed with a biologically plausible neuromuscular model. When the model included the monosynaptic-pyramidal tract, multiple peaks were obtained in about 34.5% of the motoneurons (MNs). The experimental and simulation results indicated the existence of task-dependent disparate inputs from the pyramidal tract to the MNs of the upper limb. These results suggested that intercalated interneurons are present in the spinal cord and that these interneurons might be equivalent to those identified in animal experiments.

Fast Oscillatory Commands from the Motor Cortex Can Be Decoded by the Spinal Cord for Force Control

Oscillations in the beta and gamma bands (13-30 Hz; 35-70 Hz) have often been observed in motor cortical outputs that reach the spinal cord, acting on motoneurons and interneurons. However, the frequencies of these oscillations are above the muscle force frequency range. A current view is that the transformation of the motoneuron pool inputs into force is linear. For this reason possible roles for these oscillations are unclear, since if this transformation is linear, the high frequencies in the motoneuron inputs (e.g., 20 Hz from pyramidal tract neurons) would be filtered out by the muscle and have no effect on force control. A biologically inspired mathematical model of the neuromuscular system was used to investigate the impact of high-frequency cortical oscillatory activity on force control. The model simulation results evidenced that a typical motoneuron pool has a nonlinear behavior that enables the decoding of a high-frequency oscillatory input. An input at a single frequency (e.g., beta band) leads to an increase in the steady-state force generated by the muscle. When the input oscillation was amplitude modulated at a given low frequency, the force oscillated at this frequency. In both cases, the mechanism relies on the recruitment and derecruitment of motor units in response to the oscillatory descending drive. Therefore, the results from this study suggest a potential role in force control for cortical oscillations at frequencies at or above the beta band, despite the low-pass behavior of the muscles.

SIGNIFICANCE STATEMENT

The role of cortical oscillations in motor control has been a long-standing question, one view being that they are an epiphenomenon. Fast oscillations are known to reach the spinal cord, and hence they have been thought to affect muscle behavior. However, experimental limitations have hampered further advances to explain how they could influence muscle force. An approach for such a challenge was adopted in the present research: to study the problem through computer simulations of an advanced biologically compatible mathematical model. Using such a model, we found that the well-known mechanism of recruitment and derecruitment of the spinal cord motoneurons can allow the muscle to respond to cortical oscillations, suggesting that these oscillations are not epiphenomena in motor control.

D1 and D2 Inhibitions of the Soleus H-Reflex Are Differentially Modulated during Plantarflexion Force and Position Tasks

Presynaptic inhibition (PSI) has been shown to modulate several neuronal pathways of functional relevance by selectively gating the connections between sensory inputs and spinal motoneurons, thereby regulating the contribution of the stretch reflex circuitry to the ongoing motor activity. In this study, we investigated whether a differential regulation of Ia afferent inflow by PSI may be associated with the performance of two types of plantarflexion sensoriomotor tasks. The subjects (in a seated position) controlled either: 1) the force level exerted by the foot against a rigid restraint (force task, FT); or 2) the angular position of the ankle when sustaining inertial loads (position task, PT) that required the same level of muscle activation observed in FT. Subjects were instructed to maintain their force/position at target levels set at ~10% of maximum isometric voluntary contraction for FT and 90° for PT, while visual feedback of the corresponding force/position signals were provided. Unconditioned H-reflexes (i.e. control reflexes) and H-reflexes conditioned by electrical pulses applied to the common peroneal nerve with conditioning-to-test intervals of 21 ms and 100 ms (corresponding to D1 and D2 inhibitions, respectively) were evoked in a random fashion. A significant main effect for the type of the motor task (FT vs PT) (p = 0.005, η²_p = 0.603) indicated that PTs were undertaken with lower levels of Ia PSI converging onto the soleus motoneuron pool. Additionally, a significant interaction between the type of inhibition (D1 vs D2) and the type of motor task (FT vs PT) (p = 0.038, η²_p = 0.395) indicated that D1 inhibition was associated with a significant reduction in PSI levels from TF to TP (p = 0.001, η²_p = 0.731), whereas no significant difference between the tasks was observed for D2 inhibition (p = 0.078, η²_p = 0.305). These results suggest that D1 and D2 inhibitions of the soleus H-reflex are differentially modulated during the performance of plantarflexion FT and PT. The reduced level of ongoing PSI during PT suggests that, in comparison to FT, there is a larger reliance on inputs from muscle spindles primary afferents when the neuromuscular system is required to maintain position-controlled plantarflexion contractions.

An action potential-driven model of soleus muscle activation dynamics for locomotor-like movements

OBJECTIVE

The goal of this study was to develop a physiologically plausible, computationally robust model for muscle activation dynamics (A(t)) under physiologically relevant excitation and movement.

APPROACH

The interaction of excitation and movement on A(t) was investigated comparing the force production between a cat soleus muscle and its Hill-type model. For capturing A(t) under excitation and movement variation, a modular modeling framework was proposed comprising of three compartments: (1) spikes-to-[Ca(2+)]; (2) [Ca(2+)]-to-A; and (3) A-to-force transformation. The individual signal transformations were modeled based on physiological factors so that the parameter values could be separately determined for individual modules directly based on experimental data.

MAIN RESULTS

The strong dependency of A(t) on excitation frequency and muscle length was found during both isometric and dynamically-moving contractions. The identified dependencies of A(t) under the static and dynamic conditions could be incorporated in the modular modeling framework by modulating the model parameters as a function of movement input. The new modeling approach was also applicable to cat soleus muscles producing waveforms independent of those used to set the model parameters.

SIGNIFICANCE

This study provides a modeling framework for spike-driven muscle responses during movement, that is suitable not only for insights into molecular mechanisms underlying muscle behaviors but also for large scale simulations.

Spinal mechanisms may provide a combination of intermittent and continuous control of human posture: predictions from a biologically based neuromusculoskeletal model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.

The control of upright stance is a challenging task since the objective is to maintain the equilibrium of an intrinsically unstable biomechanical system. Somatosensory information is used by the central nervous system to modulate muscle contraction, which prevents the body from falling. While the visual and vestibular systems also provide important additional sensory information, a human being with only somatosensory inputs is able to maintain an upright stance. In this study, we used a biologically-based large-scale neuromusculoskeletal model driven only by somatosensory feedback to investigate human postural control from a neurophysiological point of view. No neural structures above the spinal cord were included in the model. The results showed that the model based on a spinal control of posture can reproduce several neuromechanical outcomes previously reported in the literature, including an intermittent muscle activation. Since this intermittent muscular recruitment is an emergent property of this spinal-like controller, we argue that the so-called intermittent control of upright stance might be produced by an interplay between spinal cord properties and modulated sensory inflow.

Development of modified cable models to simulate accurate neuronal active behaviors

In large network and single three-dimensional (3-D) neuron simulations, high computing speed dictates using reduced cable models to simulate neuronal firing behaviors. However, these models are unwarranted under active conditions and lack accurate representation of dendritic active conductances that greatly shape neuronal firing. Here, realistic 3-D (R3D) models (which contain full anatomical details of dendrites) of spinal motoneurons were systematically compared with their reduced single unbranched cable (SUC, which reduces the dendrites to a single electrically equivalent cable) counterpart under passive and active conditions. The SUC models matched the R3D model's passive properties but failed to match key active properties, especially active behaviors originating from dendrites. For instance, persistent inward currents (PIC) hysteresis, frequency-current (FI) relationship secondary range slope, firing hysteresis, plateau potential partial deactivation, staircase currents, synaptic current transfer ratio, and regional FI relationships were not accurately reproduced by the SUC models. The dendritic morphology oversimplification and lack of dendritic active conductances spatial segregation in the SUC models caused significant underestimation of those behaviors. Next, SUC models were modified by adding key branching features in an attempt to restore their active behaviors. The addition of primary dendritic branching only partially restored some active behaviors, whereas the addition of secondary dendritic branching restored most behaviors. Importantly, the proposed modified models successfully replicated the active properties without sacrificing model simplicity, making them attractive candidates for running R3D single neuron and network simulations with accurate firing behaviors. The present results indicate that using reduced models to examine PIC behaviors in spinal motoneurons is unwarranted.

Influences of premotoneuronal command statistics on the scaling of motor output variability during isometric plantar flexion

This study focuses on neuromuscular mechanisms behind ankle torque and EMG variability during a maintained isometric plantar flexion contraction. Experimentally obtained torque standard deviation (SD) and soleus, medial gastrocnemius, and lateral gastrocnemius EMG envelope mean and SD increased with mean torque for a wide range of torque levels. Computer simulations were performed on a biophysically-based neuromuscular model of the triceps surae consisting of premotoneuronal spike trains (the global input, GI) driving the motoneuron pools of the soleus, medial gastrocnemius, and lateral gastrocnemius muscles, which activate their respective muscle units. Two types of point processes were adopted to represent the statistics of the GI: Poisson and Gamma. Simulations showed a better agreement with experimental results when the GI was modeled by Gamma point processes having lower orders (higher variability) for higher target torques. At the same time, the simulations reproduced well the experimental data of EMG envelope mean and SD as a function of mean plantar flexion torque, for the three muscles. These results suggest that the experimentally found relations between torque-EMG variability as a function of mean plantar flexion torque level depend not only on the intrinsic properties of the motoneuron pools and the muscle units innervated, but also on the increasing variability of the premotoneuronal GI spike trains when their mean rates increase to command a higher plantar flexion torque level. The simulations also provided information on spike train statistics of several hundred motoneurons that compose the triceps surae, providing a wide picture of the associated mechanisms behind torque and EMG variability.

Plantar flexion force induced by amplitude-modulated tendon vibration and associated soleus V/F-waves as an evidence of a centrally-mediated mechanism contributing to extra torque generation in humans

Background

High-frequency trains of electrical stimulation applied over the human muscles can generate forces higher than would be expected by direct activation of motor axons, as evidenced by an unexpected relation between the stimuli and the evoked contractions, originating what has been called “extra forces”. This phenomenon has been thought to reflect nonlinear input/output neural properties such as plateau potential activation in motoneurons. However, more recent evidence has indicated that extra forces generated during electrical stimulation are mediated primarily, if not exclusively, by an intrinsic muscle property, and not from a central mechanism as previously thought. Given the inherent differences between electrical and vibratory stimuli, this study aimed to investigate: (a) whether the generation of vibration-induced muscle forces results in an unexpected relation between the stimuli and the evoked contractions (i.e. extra forces generation) and (b) whether these extra forces are accompanied by signs of a centrally-mediated mechanism or whether intrinsic muscle properties are the predominant mechanisms.

Methods

Six subjects had their Achilles tendon stimulated by 100 Hz vibratory stimuli that linearly increased in amplitude (with a peak-to-peak displacement varying from 0 to 5 mm) for 10 seconds and then linearly decreased to zero for the next 10 seconds. As a measure of motoneuron excitability taken at different times during the vibratory stimulation, short-latency compound muscle action potentials (V/F-waves) were recorded in the soleus muscle in response to supramaximal nerve stimulation.

Results

Plantar flexion torque and soleus V/F-wave amplitudes were increased in the second half of the stimulation in comparison with the first half.

Conclusion

The present findings provide evidence that vibratory stimuli may trigger a centrally-mediated mechanism that contributes to the generation of extra torques. The vibration-induced increased motoneuron excitability (leading to increased torque generation) presumably activates spinal motoneurons following the size principle, which is a desirable feature for stimulation paradigms involved in rehabilitation programs and exercise training.